返回题库

HMMT 二月 2009 · CALC 赛 · 第 5 题

HMMT February 2009 — CALC Round — Problem 5

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 4 ] Compute ( ) ( ) ( ) ( ) ( ) π π π π π sin + 4 h − 4 sin + 3 h + 6 sin + 2 h − 4 sin + h + sin 3 3 3 3 3 lim . 4 h → 0 h
解析
  1. [ 4 ] Compute ( ) ( ) ( ) ( ) ( ) π π π π π
  • 4 h − 4 sin + 3 h + 6 sin + 2 h − 4 sin + h + sin sin 3 3 3 3 3 lim 4 h → 0 h √ 3 Answer: 2 f ( x + h ) − f ( x ) ′ Solution: The derivative of a function is defined as f ( x ) = lim . Iterating this h → 0 h formula four times yields f ( x + 4 h ) − 4 f ( x + 3 h ) + 6 f ( x + 2 h ) − 4 f ( x + h ) + f ( x ) (4) f ( x ) = lim . 4 h → 0 h √